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lieven lebruyn
mathematician by day, blogger by night
mathematician by day, blogger by night

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le Tour de France in Grothendieck's backyard

If you want to see the scenery Grothendieck enjoyed in his later years, watch the Tour de France tomorrow.
It starts in Saint-Girons where he went to the weekly market [0] (and died in hospital, november 13th 2014), ending in Foix with 3 category 1 climbs along the way (familiar to anyone familiar with Julia Stagg's expat-lit set at 'Fogas' [1],[2]).
It will not pass through Lasserre [3] (where G spend the final 20 years of his life) which is just to the north of Saint-Girons.

#Grothendieck #Ariege #France

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Buy a Grothendieck painting to get the Lasserre notes online!

As of yesterday, most of Grothendieck's Montpellier notes are freely available at
There's much to say about the presentation (eg. It is not possible to link directly to a given page/article, it is scanned at only 400 dpi etc. etc.) but hey, here they are at last, for everyone to study.
By far the most colourful (in my first browsing of the archive) is cote No. 154, on 'systeme de pseudo-droites'. You can download it in full (a mere 173 Mb).
As you know, the Montpellier notes are only a fraction of the material Grothendieck left behind. By far the largest (though probably not the most interesting, mathematically) are the Lasserre notes, which to the best of my knowledge are in the care of a Parisian bookseller.
Here's an idea:
almost every page of No. 154 (written on ancient computer-output) looks like a painting. No doubt, most math departments in the world would love to acquire one framed page of it. Perhaps this can raise enough money to safeguard the Lasserre notes...


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For all of you waiting for Grothendieck's Montpellier notes to be released tomorrow, the address is as of 18.00 GMT May 10th:

I've just received the following mail:

Chères toutes et tous,

J’ai le plaisir de vous annoncer qu’après des mois de négociations, nous allons être en mesure de diffuser une partie significative (18000 pages / 28000) du fonds d’archives Alexander Grothendieck de Montpellier. Une cérémonie / conférence de presse est prévue demain (mercredi 10 mai) en fin d’après-midi à l’Université de Montpellier.

L’adresse du site dédié est la suivante:

Pour l’instant l'accès est bloqué par un mot de passe, les 18000 pages seront consultables et téléchargeables librement dès demain 18h.

N’hésitez pas à communiquer cette information aux membres de vos laboratoires.

Bien amicalement,

Jean-Michel Marin
Directeur de l’Institut Montpelliérain Alexander Grothendieck

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Grothendieck's Montpellier notes will hit the net May 10th

At last there is an agreement between the university at Montpellier and Grothendieck's children to release the 'Montpellier gribouillis' (about 28000 pages will hit the net soon).
Another 65000 pages, found at Lasserre after Grothendieck's death, might one day end up at the IHES or the Bibliotheque Nationale.
If you are interested in the history of Grothendieck's notes, there is this old post on my blog:

(h/t Theo Raedschelders for the Liberation link)

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Nice Quanta-article on the cosmic Galois group.

Here's the arXiv paper by Francis Brown on which it is based:
Here's some info about the cosmic group at the nLab:
And an older arXiv note by Jack Morava:

Quanta: "Brown is looking to prove that there’s a kind of mathematical group — a Galois group — acting on the set of periods that come from Feynman diagrams. “The answer seems to be yes in every single case that’s ever been computed,” he said, but proof that the relationship holds categorically is still in the distance. “If it were true that there were a group acting on the numbers coming from physics, that means you’re finding a huge class of symmetries,” Brown said. “If that’s true, then the next step is to ask why there’s this big symmetry group and what possible physics meaning could it have.”

Among other things, it would deepen the already provocative relationship between fundamental geometric constructions from two very different contexts: motives, the objects that mathematicians devised 50 years ago to understand the solutions to polynomial equations, and Feynman diagrams, the schematic representation of how particle collisions play out. Every Feynman diagram has a motive attached to it, but what exactly the structure of a motive is saying about the structure of its related diagram remains anyone’s guess."

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The Hallucinated Stacks Project

Andrej Karpathy has a nice blog post on "The Unreasonable Effectiveness of Recurrent Neural Networks" [1]. He gives examples of how such networks can deal with Shakespeare, Wikipedia, Linux source code, baby names and... algebraic geometry!

here's what you can expect when you feed a recurrent neural network the entire Stacks project [2]. 

"We downloaded the raw Latex source file (a 16MB file) and trained a multilayer LSTM. Amazingly, the resulting sampled Latex almost compiles. We had to step in and fix a few issues manually but then you get plausible looking math, it's quite astonishing:"

about what you might expect of an unguided student who stumbles upon the project. they might be slightly better at hallucinating plausible diagrams though...

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via reddit/m

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where are the videos of the Grothendieck conference?

Mid june 2015 a conference "Mathematics of the 21st century: the vision of Alexander Grothendieck'' was held in Montpellier [1]. In a comment to a post here on Maltsiniotis' talk [2] i mentioned that most of the talks were video-taped and that they would soon be made public.

When they failed to surface on the Montpellier website, i asked +Damien Calaque  for more information. Some months ago Damien told me the strange (and worrying) tale of their fate.

At that moment Damien was in a process of trying to recover the videos. Two weeks ago he told me things were looking good, so i now feel free to post about it.

Michael Wright is the head of the Archive for Mathematical Sciences & Philosophy [3]. He arranged with the organizers of the conference that he would send someone over to video-tape the lectures and that he would make them available on his Archive. He also promised to send a copy of the videos to Montpellier, but he never did. Nor did the tapes appear on his site.

Damien Calague emailed Wright asking for more information and eventually got a reply. It appears that Wright will not be able to edit the videos nor put them online in a reasonable time.

They agreed that Damien would send him a large capacity USB-drive. Wright would copy the videos on it and send it back. Damien will arrange for the videos to be edited and the University of Montpellier will put them online. Hopefully everything will work out smoothly.

So please keep an eye on the website of l'Institut Montpelliérain Alexander Grothendieck:

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Psst : the 49th Mersenne prime was discovered 12 days ago. 

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I just love Woit's final paragraph:

"I’m actually in a way more sympathetic than most people to the idea that “non-empirical” evaluation of a theory is an important and worthwhile topic. Fundamental physics theory is facing a huge problem due to the overwhelming success of the Standard Model and the increasing difficulty of exploring higher energy scales. If it is to continue to make progress there is a real need to do a better job of evaluating theoretical ideas without help from experiment. There is a group of scientists who have a lot of experience with this problem, and have a well-developed culture designed to deal with it. They’re called “mathematicians”. Despite the fact that this workshop is hosted by the Munich Center for Mathematical Philosophy, the organizers don’t seem to have thought it worthwhile to invite any mathematicians or mathematical physicists to participate, missing out on a perspective that would be quite valuable."

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Did Chevalley invent the Zariski topology?

In his inaugural lecture at #ToposIHES Pierre Cartier stated (around 44m11s):
"By the way, Zariski topology, as we know it today, was not what Zariski invented. He invented a variant of that, a topology on the set of all valuation rings of a given field, which is not exactly the same thing. As for the Zariski topology, the rumour is that it was invented by Chevalley in a seminar given by Zariski, but I have no real proof."
Do you know more about this?

Btw. the full lecture of Cartier (mostly on sheaf theory) is not on the IHES YouTube channel, but on the channel of +Laurence Honnorat:

The IHES did begin to upload videos of the remaining plenary talks at (so far, the wednesday talks are availble).
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